feat(Combinatorics/SimpleGraph/Paths): existence of a shortest cycle at a vertex

[SnirBroshi]

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Longest paths/trails/cycles/circuits are handled in #41522

For circuits not fixed to a specific vertex we have exists_girth_eq_length and IsCircuit.girth_le_length.

A shortest circuit is a cycle and every cycle is a circuit, so there's no reason to have separate circuit/cycle versions, unlike the "longest" versions.

Note that the notion of shortest paths/trails (either globally or from a specific vertex) doesn't make sense because the nil walk is a path/trail. However a shortest path/trail between two specific endpoints does make sense, and we have Reachable.exists_path_of_dist and dist_le for that case.

[github-actions]

PR summary 1450ccebb1

Import changes for modified files

No significant changes to the import graph

Import changes for all files

Files	Import difference

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Declarations diff (regex)

+ exists_isCycle_forall_isCircuit_length_le_length

You can run this locally as follows

## from your `mathlib4` directory:
git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci

## summary with just the declaration names:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh <optional_commit>

## more verbose report:
../mathlib-ci/scripts/pr_summary/declarations_diff.sh long <optional_commit>

The doc-module for scripts/pr_summary/declarations_diff.sh in the mathlib-ci repository contains some details about this script.

Declarations diff (Lean)

✅ Lean-aware diff — post-build, computed from the Lean environment (commit 1450cce).

• +1 new declarations
• −0 removed declarations

+SimpleGraph.Walk.exists_isCycle_forall_isCircuit_length_le_length

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No changes to strong technical debt.

No changes to weak technical debt.

Current commit 1450ccebb1
Reference commit 1f165a51de

This script lives in the mathlib-ci repository. To run it locally, from your mathlib4 directory:

git clone https://github.com/leanprover-community/mathlib-ci.git ../mathlib-ci
../mathlib-ci/scripts/reporting/technical-debt-metrics.sh pr_summary

• The relative value is the weighted sum of the differences with weight given by the inverse of the current value of the statistic.
• The absolute value is the relative value divided by the total sum of the inverses of the current values (i.e. the weighted average of the differences).